Reliability evaluation of an aggregate battery energy storage system in microgrids under dynamic operation

Electrical Power and Energy Systems 118 (2020) 105786

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Reliability evaluation of an aggregate battery energy storage system in microgrids under dynamic operation

T

Trang Thi Phama, Tsai-Chi Kuoa,c,d, , Duong Minh Buib ⁎

a

Department of Industrial and Systems Engineering (ISE), Chung Yuan Christian University (CYCU), Taiwan Department of Electrical Engineering and Information Technology (EEIT), Faculty of Engineering, Vietnamese-German University (VGU), Thu Dau Mot City, Binh Duong, Viet Nam c R&D Center for Membrane Technology, Chung Yuan Christian University (CYCU), Taoyuan, Taiwan d Department of Industrial Management, National Taiwan University of Science and Technology, Taipei 10607, Taiwan b

ARTICLE INFO

ABSTRACT

Keywords: Reliability evaluation Battery energy storage systems Microgrid Dynamic operation Repair and failure rates

A microgrid (MG) which mainly consists of distributed generators (DGs) and energy storage systems (ESSs), is deployed to supply power for local loads. Distributed generators are mostly renewable energy sources. An aggregate system with multiple battery energy storage devices that should be used to improve the reliability of power supply from these renewable energy sources in the MG, is defined as an aggregate battery energy storage system (ABESS). The ABESS is used to control the source-load power balance so that the MG can operate at high stability and reliability to supply electricity for different customers. To demonstrate the significance of the ABESS in the MG, its operation reliability will be analyzed in this paper. A systematic method is proposed to evaluate reliability performance of the ABESS under different dynamic operation cases in the MG. Specifically, an analytic approach based on Markov models is developed to assess the operation reliability of the whole ABESS. Besides the used-time-dependent failure rates, voltage-fluctuation and power-loss dependent failure rates (VF-PL DFR) of critical components of the ABESS such as bidirectional DC/DC converters, DC/AC inverters, switching and protective devices, battery modules, and battery charger/controller are also formulated and incorporated in the reliability evaluation. According to differently dynamic operation cases of a microgrid with the ABESS and photovoltaic (PV) generation systems, the VF-PL DFR of the ABESS will be variously affected. Randomly dynamic operation scenarios of the MG are analyzed including: change in load power, the intermittent and unstable operation of PV sources, on/off-grid operation modes of the microgrid, and discharging and charging states of the ABESS. Simulation test results are presented and discussed to validate that the operation reliability of the ABESS in the microgrid significantly depends on its differently dynamic operation strategies along with the applied voltage stress.

1. Introduction 1.1. Motivation Renewable energy sources (RESs) have been strongly developed in recent years as an effectively alternative selection for conventional energy sources. A small power system with integration of renewable energy sources along with different loads and energy storage devices is also called a microgrid [1]. Multiple microgrids are interconnected in a larger power system where is called a local energy community (LEC). A microgrid can be built in household or community sizes. The electricity generation of RESs is definitely intermittent and unstable due to the nature, so energy storage devices should be certainly used to dispatch

⁎

the power flow between renewable energy sources and loads so that the MG operation can get high stability and reliability of power supply. Energy storage systems will store the surplus electricity from RESs, and then release that electricity to customers when required. For household-sized microgrids, the amount of power is quite low such that it could not meet load demands of different customers. Therefore, the customers will have to buy electricity from their neighbor microgrids or buy electricity directly from the grid. However, buying and selling the electricity among the customers with microgrids will be a big challenge. One of main reasons is that the power demand of customers is quite different from each other, so it could be difficult to exactly determine the redundant amount of microgrid power of the customers to perform buying/selling the electricity. The next reason is

Corresponding author at: Department of Industrial and Systems Engineering (ISE), Chung Yuan Christian University (CYCU), Taiwan. E-mail addresses: [email protected], [email protected] (T.T. Pham), [email protected] (T.-C. Kuo), [email protected] (D.M. Bui).

https://doi.org/10.1016/j.ijepes.2019.105786 Received 27 August 2019; Received in revised form 24 November 2019; Accepted 13 December 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

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that power exchange among the customers could not get high reliability and stability. Last but not least, buying the electricity directly from the grid may not be encouraged for the customers because the efficient use of renewable energy sources is a priority energy policy for most countries [2]. In summary, to overcome the above challenge, it is necessary to develop an aggregate energy storage system in order to store the excess energy produced by RESs in household-sized microgrids and release when the energy production of RESs are less than the energy demand of the customers. Energy storage systems can be divided into two categories, including household energy storage (HES) and aggregate energy storage (AES). Although the total power amount of a household-sized microgrid is quite small at few kilowatts, the investment cost is a possible downside for the HES system. Therefore, it is not incentive to deploy the HES system for households. On the other hand, the AES system is a community-sized energy storage system which will be a promising selection for large-sized microgrids. The AES system will buy the electricity from the households/customers with microgrids when their power consumption is redundant, while it will sell the electricity to other households/customers in certain times. From the above viewpoint, the significance of the AES system for microgrids is not doubtful. The operation of the AES system should be continuous and stable so that it is possible to limit power interruption to the customers [3]. To do that, it is needed to take into account to the operation reliability of the AES system in microgrids, which will be analyzed in this paper.

In [10,16], an overview of publications related to the use of battery technology for wind generation systems has been presented. In [17,18], battery energy storage technologies (including lead-acid, nickel cadmium, nickel metal hydride, and lithium ion) for small-scaled renewable energy applications have been practically and comprehensively assessed according to their technical merit and economic feasibility. In [19,25], a microgrid with BESS and PV systems has been analyzed at three operational modes, mainly, charging stage of the battery; the battery system in a standby mode; and discharging state of the battery. In [20], flywheels, capacitors, and batteries are most suitable to manage the intermittent and unstable operation of RESs. In [13,21], a detailed analysis of real-life application and performance of batteries energy storage technologies has been mentioned. In [22,23], the selection of battery technologies to support grid-connected renewable energy sources has been discussed by evaluating the energy-to-power (E/P) ratio. In summary, it is conceivable that battery energy storage applications for microgrids with RESs will continue to be enlarged in future. Regarding the integration of battery energy storage technologies into the microgrids with RESs, it is obviously seen that efficiency, cost-effectiveness, technology, as well as operation reliability of the BESS in the MG should be considered in detail. 1.2.2. Reliability studies on battery energy storage systems Several research results on the reliability evaluation of BESS have been published [26–39]. In [26], a reliability assessment model of BESS is based on the state of health of battery cells, which is a function of the battery module power in the ith charging/discharging cycle, the equivalent number of charging/discharging cycles, the initial battery module capacity, and the duration of the ith cycle. The model is analyzed by a universal generating function-based method. However, this model is only focused on reliability evaluation of battery modules and converter modules under different topologies of the BESS. Besides for considering BESS topologies, it is necessary to study on dynamic operation cases of the BESS for reliability performance. In [27,28], there are research efforts on reliability evaluation of wind generation systems along with energy storage. In [29], a probabilistic method is proposed to evaluate the reliability of standalone wind energy systems, but the reliability of battery storage systems is not highly focused. In [30,31], reliability analysis of battery packs in a BESS has been reported. The reliability evaluation of battery packs under different configurations and redundancy structures are mainly focused. In [39], a reliability model of lithium-ion battery packs is modified which consists of multiphysics models, degradation models, and a multistate-system reliability model. Regarding the degradation models, a stochastic capacity degradation model and a dynamic response impedance model with degradation and changing temperature are empirically build-up. The system-level reliability model of the battery pack can be established by a reliability block diagram. The universal generating function is also used to analyze the reliability of battery packs. In general, there are very few research papers to do reliability assessment of all critical components (e.g. battery packs, converter modules, and battery configurations) in the BESS under dynamic operation schemes. Therefore, reliability models being appropriate for battery modules, power converters, battery configurations and protective devices are all of importance to the reliability evaluation of the whole ABESS under dynamic operation. In [32], a mobile battery energy storage system (MBESS) is used to enhance the operation reliability of distribution system. A Markovbased analytic approach is applied for assessing the reliability of MBESS. However, power converter modules and different topologies of the MBESS have not been analyzed in the evaluation. In [33–35], the comprehensive reliability assessment of distribution system is performed considering penetration of wind-turbine generation system (WTGS), energy storage system (ESS), and photovoltaic (PV) generating system. A Markov model is also proposed to assess reliability of main components of renewable energy sources and the ESS. However,

1.2. Literature review 1.2.1. Overview of battery energy storage systems Reference [4] has listed common energy storage technologies which could be used for the aggregate energy storage (AES) system, such as: Pumped Hydro Storage (PHS), Compressed Air Energy Storage (CAES), Flywheel Energy Storage, Lead Acid Battery, Nickel Cadmium Battery, Lithium Ion Battery, Sodium Sulphur Battery, Sodium Nickel Chloride Battery, Vanadium Redox Battery, Zinc Bromine Battery, Polysulphide Bromide Batteries, Superconducting Magnetic Energy Storage, Supercapacitor, Hydrogen, Synthetic Natural Gas, and Thermal Energy Storage. These energy storage technologies can be divided into five categories according to the type of stored energy, consisting of mechanical, electrical, thermal, electro-chemical and chemical energy storage technologies. Mechanical storage technologies are developed to store energy in forms of potential and kinetic energy, e.g. CAES and PHS [5–7]. Electrical storage technologies are applied to store energy in the forms of electrostatic, mainly including capacitors, super-capacitors (SC), or superconducting magnetic energy storage (SMES) system [8–10]. Chemical-energy-related storage technologies contain chemical energy storage (e.g. batteries), electrochemical energy storage (e.g. hydrogen fuel cells, solid oxide fuel cells), and thermochemical energy storage (e.g. solar hydrogen, solar metal, solar ammonia, or solar methane) [11–13]. In general, batteries and fuel-cells are the most commonly storage options for applications related to renewable energy sources in the MG. To store electrical energy in a large scale, it is almost possible to exploit pumped hydro storage technology. However, this PHS technology can significantly affect ecological systems. Therefore, emerging storage technologies, e.g. batteries, capacitors and super-capacitors, flywheels, and others are being continuously developed in recent times, which not only provide the reliability of energy storage with low cost but also support fast demand response and scalability [14,15]. Specifically, the battery technology has become one of the most popular and cost-effective energy storage technologies, which is available for power system applications like microgrids [10,13,16–23]. Battery energy storage systems (BESS) can provide flexible storage capacity levels and technical benefits, which could be located at any expected locations on the grid/microgrid [16]. Moreover, reference [24] has presented several practical applications of battery energy storage in recent years. 2

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determination of failure and repair rates of main components of RESs and ESSs under dynamic operation conditions has not been considered. It means that failure and repair rates of WTGS, ESS, and PV units only depend on their used time [36,37]. In [38], a novel probabilistic model of BESS is proposed to implement analytical technique for reliability assessment of microgrids with RES and BESS. However, the reliability of main components of the RES and the BESS has not evaluated. Additionally, there are some recent researches on reliability evaluation of the BESS. To be more detailed, in [40], the reliability assessment of a PV-battery hybrid system is presented. Although the paper provides the valuable information about differences in the electrical and thermal loading to the reliability level of the PV-battery system, only the most reliability-critical components among power electronic units, e.g. switching devices, DC/DC converters, and DC/AC inverters, are analyzed during the reliability evaluation performance. Moreover, the effect of dynamic operation cases on the time-used dependent failure rates (TDFR) of the PV-battery system during the operating time has also not been mentioned in detail. In [41,42], reliability models have been developed to evaluate advantages related to WTGS and ESS in the power system. A Monte Carlo Simulation (MCS) method incorporates dynamic operating strategies of the WTGS and the ESS for the system-level reliability evaluation. In [43], a novel analytical technique is developed to assess the reliability of distribution networks through the evaluation of battery energy storage contribution. This technique uses a probabilistic model of energy storage to evaluate the charging and discharging processes over a fault duration and the relevant operational strategy. From a literature review for reliability studies on the BESS, the following conclusions can be drawn, such as: (i) necessity to evaluate the operation reliability of main components of an ABESS in microgrids under dynamic operation conditions, including the sudden change in load power, unstable and intermittent operation of RES, the on/off-grid operation modes of the microgrid, and discharging and charging states of the ABESS; (ii) an analytic approach based on Markov models commonly applied for assessing the BESS’s reliability; and (iii) necessity to determine the failure/repair rates of main components of the whole ABESS depending on voltage fluctuation, power loss and their used time.

fuses, circuit breakers, relays), diodes, capacitors, and bidirectional DC/ AC and DC/DC converters have been theoretically analyzed in detail. Section 3 describes a common method to build discrete probability distribution. Section 4 presents the reliability analysis based on Markov models of the entire ABESS. A microgrid simulation model with the ABESS and PV system is mentioned in Section 5. Dynamic operation cases of the microgrid with the ABESS are performed to figure out failure rates of the ABESS. Reliability testing results of the ABESS are analyzed and discussed in Section 6, followed by conclusions in Section 7. 2. Reliability models of main components in an aggregate battery energy storage system 2.1. Reliability evaluation of battery modules A reliability model of battery modules (BM) is represented by a twostate model with up and down states according to the unit failure. Forced Outage Rate (FOR) that is mostly called the unavailability of an n-th battery module is given by Eq. (1).

FORnBM =

BM n BM n

+ µnBM

(1)

where λ and μ are failure and repair rates, respectively. With failure of the n-th battery module, probabilities of the two states are shown in Eq. (2).

ftBM (x ) =

FORnBM , x = PtBM

1

FORnBM , x = 0

(2)

where PtBM is the power of a battery module, which can increase to its BM maximum value Pmax and limit to the rated power of the BM.

PtBM

=

CtBM t

BM × SOCt , SOCt < Pmax ×

t CtBM

BM Pmax , otherwise

(3)

In Eq. (3), PtBM is the available output power of the BM during the charging/discharging time t , CtBM is the degraded capacity and SOCt is the state of charge (SOC) of the BM at a time t. Battery modules can be configured by various battery types such as: Lead acid, Ni-MH, Ni-Cd, Li-ion with slightly different life-cycle characteristics. The aging of batteries depends on different factors, mainly, the number of charging/ discharging cycles, over-charging or over-discharging, temperature conditions, and the depth of discharge [17,18]. However, the average SOC, SOC Avg , and SOC swing, SOC Swg , are two most important parameters impacting on the degradation state of the battery operation [44]. The SOC shows a ratio of the charged capacity in the range between 0% and 100% indicating the completely discharged and fully charged states of the battery, respectively. The SOC swing shows a change in the SOC level related to one cycle of charging and discharging. Eq. (4) represents a relationship between SOC Avg , SOC Swg and the number of available charging/discharging cycles, NCBM , for the lifetime of the battery [44].

1.3. Contributions This paper proposes a systematic method to evaluate reliability performance of the whole ABESS considering differently dynamic operation conditions. Besides the used-time-dependent failure rates (TDFR), voltage-fluctuation and power-loss dependent failure rates (VFPL DFR) of main components in the whole ABESS (including bidirectional DC/DC converters, DC/AC inverters, switching and protective devices, battery modules, battery charger/controller) are formulated and incorporated in the reliability evaluation. Reliability analysis of the ABESS is implemented in a microgrid with PV generation systems. Randomly dynamic operation scenarios of the ABESS and the PV system in the microgrid are designed and simulated by PSCAD software. Moreover, a Markov-based analytic approach is used to assess the operation reliability of the entire ABESS in the microgrid. Common failure density functions could be properly selected for failure rates of the ABESS’s components during the reliability assessment. Simulation test results are presented and discussed to validate that the operation reliability of the ABESS in the microgrid significantly depends on differently dynamic operating strategies along with applied voltage stress.

ln NCBM (SOC Swg , SOC Avg ) =

1.453 ln SOC Swg

3.6SOC Avg + 9.547 (4)

NCtBM

1.4. Structure of the paper

(SOCtSwg ,

SOCtAvg = (SOCt

t

SOCt

t

SOCtSwg =

The remainder of this paper is organized as the following. Reliability models of main components of the ABESS are proposed in Section 2. Specifically, reliability assessments of battery modules, battery topologies, switching and protective devices (consisting of IGBTs,

SOCt

Avg

)=

(SOCtSwg ) 1.453

+ SOCt ) 2

SOCt t

×e

3.6SOCtAvg

× 14003

(5) (6) (7)

The battery operation is limited to a SOC level of 50%. Therefore, an aging ratio (AR) of the battery per cycle is given by Eq. (8), where the aging ratio is inversely proportional to the number of available cycles. 3

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0.5 NCtBM (SOCtSwg , SOCtAvg )

ARt =

BM is the nominal or rated capacity of battery module which is a with Crated standard value given by the manufacturer to characterize the battery type; C is a temperature coefficient of the battery commonly selected at 0.6%/0C [47]. Generally, the failure rate of battery module depends on its available capacity. The battery capacity is a function of the number of cycles. The number of operation cycles is a function of the average SOC and the SOC swing. The SOC level is highly dependent on the battery voltage and current, efficiency, and the charging/discharging time. However, during dynamic operation conditions of the BM, the battery voltage is the most important parameter used to calculate the SOC level as well as the failure rate of battery module, BM . In addition, the repair rate of battery module, , is selected at a constant value in this paper.

(8)

The BM capacity, CtBM is calculated by Eq. (9), where C0BM is the initial capacity of battery module and CdBM is the capacity degradation ratio at the ending time of the battery life-cycle.

CtBM = C0BM × 1

CdBM ×

t

t

ARt

(9)

t=1

Under the charging/discharging operation, the SOC of battery is accordingly updated and calculated by Eq. (10), where BM is the battery efficiency, is the self-discharge rate of the battery at about 0.2%/ day [45].

SOCt = SOCt

t

× 1

SOCt = SOCt

t

× 1

24

24

PtBM

t +

BM

CtBM

VtBM ItBM

t +

CtBM

t

BM

2.2. Reliability evaluation of battery topologies

(10)

t

A battery energy storage system mainly contains battery modules, power electronic converters and a battery energy management system. According to the desired output voltage and the capacity of battery modules (BM), multiple battery cells are connected in series or in parallel or both. Similarly, depending on the desired output voltage and the capacity of a battery array (BA), multiple battery modules are connected in series or in parallel or both. For a basic configuration of BESS, the battery modules are connected in series to form a battery string (BT). More strings are connected in parallel to form a battery array. A battery energy storage system is a parallel combination of all battery arrays, as referred to Fig. 1. BESS The probability of BESS, pup , being in an operating (up) state could be determined by Eq. (15) where RBM is the reliability of a battery module; Ni is the total number of BMs connected in series in a battery string; Mj is the total number of battery strings connected in parallel of a battery array (BA); and K z is the total number of battery arrays in a BESS.

(11)

where is the terminal voltage of BM, and is the charging/ discharging current of BM at the time t. ItBM is positive for the charging mode and is negative for the discharging mode. An empirical formula recommend by FIDES Guide 2009 could be used to evaluate the failure rate of battery modules [46], as the following:

ItBM

VtBM

BM

=

×

Physical

=

0_Battery

×( ×

PM

×

Pr ocess

× NCells ×

Thermal - Electrical

PM

×

Pr ocess

+

+

wear - out

Phases i=1

+

TCy

(

)

tannual 8760 i

+

Mechanical )i

×(

Induced )i

(12)

wear - out

where, is the failure rate due to the physical contribution; wear - out is the wear-out failure rate, selected at the range of 0.1–0.2; PM represents the quality and technical control over manufacturing of the item, selected a default value of 1.7; Pr ocess represents the quality and technical control over the development, manufacturing and usage process for the product, selected a default value of 4.0; 0_Battery is the basic failure rate related to the subassembly, selected at the value of 0.25; NCells is the number of battery cells in a battery module; tannual is the time for each operating phase over a year; Thermal - Electrical , TCy , and Mechanical are acceleration factors related to physical overstresses of thermal and electrical, temperature cycling, and mechanical origin, respectively. TCy is selected at 0.14 and Mechanical is selected at 0.01. Induced represents the contribution of overstresses caused by other factors in an application field, properly selected from 1 (for the best case) to 100; The ‘Phases’ variable represents the number of charging/discharging phases of battery per year. BM , and the Thermal - Electrical is a function of the Celsius temperature, Tt available capacity, CtBM , of the battery, which is calculated by Eq. (13) at the time t.

BESS pup =1

Physical

(

Thermal - Electrical )t

= 0.85 × e

4642 ×

1 293

1 TtBM

TtBM =

CtBM BM Crated C

BM C (Tt

Mj

1

j=1

1

Ni

RiBM

(15)

i=1

In this section, failure rates of switching devices using discrete semiconductors (e.g. IGBT, MOSFETs) and protective devices (e.g. fuses, circuit breakers and relays) are studied in detail. 2.3.1. Failure rates of switching devices Isolation gate bipolar transistors (IGBTs) are commonly used in the switching operation of power converters or can be worked as circuit breakers. According to FIDES Guide 2009, the failure rate of the IGBT could be calculated as follows: IGBT

=

0TH FThermal

FRH +

+

0TCyCase FTCyCase

0Mech FMech )

Induced

PM

+

0TCySJ FTCySJ

Process

+

0RH

(16)

where 0TH is the basic failure rate of IGBT due to the thermal overstress, 0TCyCase is the failure rate due to the thermal cycling effect on case, 0TCySJ is the failure rate due to the thermal cycling effect on solder joint, 0RH and 0Mech are failure rates related to humidity and mechanical overstress, respectively. FThermal , FTCyCase , FTCySJ , FRH and FMech acceleration factors related to physical overstresses of electrical, thermal, and mechanical effects, respectively. Induced describes overstresses caused by other factors. PM represents the quality and technical control of manufactured parts. Pr ocess represents the quality and technical control over reliability in the product life-time. The detailed values of these factors are found in the reference [46]. To describe relationship between the voltage and the failure rate of IGBT, a thermal factor, FThermal , is expressed as follows:

(13)

298.15))

1

+ 298.15

1

2.3. Reliability evaluation of switching and protective devices

where TtBM is expressed by Eq. (14) as follow: BM CtBM = Crated (1 +

Kz z=1

(14) 4

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T.T. Pham, et al.

Fig. 1. A basic configuration of the BESS.

FThermal = FElectrical . e

11604 × 0.7 ×

1 293

1 (Tj + 273)

current of the fuse. Generally, it can be seen that the failure rate of fuses is a basic function of temperature and current.

(17)

where Tj is the junction temperature of the IGBT; and FElectrical is an electrical factor of the IGBT given by Eq. (18).

FElectrical =

b) Failure rates of circuit breakers Circuit breakers (CB) are used to close/open a BESS at full-load (normal) or fault operation modes. The failure rate of a CB or a switch is calculated by Eq. (21) [46].

(VApplied Vr , IGBT ) 2.4 if(VApplied Vr , IGBT ) > 0.3 0.056 if(VApplied Vr , IGBT )

0.3

(18)

where VApplied is the applied voltage across the IGBT during its operation performance; and Vr , IGBT is the rated reverse voltage of the IGBT shown by the manufacturer. In general, it is worth noting that the failure rate of IGBT is a basic function of voltage and temperature. The temperature depends on the power loss of the IGBT while the voltage is fluctuated according to dynamic operation cases of the IGBT.

CB

=[

a) Failure rates of fuses The reliability evaluation of fuses is a unique problem because there is very little correlation between the replacement of fuse and its failure. When a fuse opens and must be replaced, it can be obviously understood that the fuse has satisfactorily performed its protective function. Otherwise, it is necessary to predict the reliability of the fuse in case which the fuse has not opened when it should be opened. According to FIDES Guide 2009, the failure rate of fuses, FUSE , could be calculated as follows:

Electrical

×

×(

Induced ]

Thermal Electrical

×

PM

×

+

TCy

+

Mechanical

+

RH

+

IApplied 1 × 0.8 Ir , Fuse

× e

11604 × 0.15 ×

1 293

1 TFuse + 273

+

Electrical

+

TCy

+

Mechanical

+

RH )

×

Induced ]

(21)

= 0.59 × CEL ×

pole

×

EL _break

×

load type

×

manoeuvres

× SVn (22)

If Vapplied Vnominal > 1, then n = 8.8 If Vapplied Vnominal

1, then n = 3

(23)

with Vapplied is the applied voltage across the CB, and Vnominal is the nominal voltage of the CB.

SIm = (Iapplied Inominal )m If Iapplied Inominal > 1, then m = 5.9 If Iapplied Inominal

Thermal Electrical

= 0.13 ×

Process

SVn = (Vapplied Vnominal )n

Chi )

where Thermal Electrical , TCy , Mechanical , RH , and Chi are acceleration factors related to thermal, electrical, thermal cycling, mechanical, relative humidity, and environmental effects, respectively. 0_Fuse is the basic failure rate associated with main components of the fuse. The thermal-electrical factor, Thermal Electrical , is expressed as follows: 1.5

Thermal

×

where CEL is selected from 0.56 to 1.19, pole is a factor depending on the number of poles and contact type (2–2.5); EL _break is a factor related to the breaking capacity at 1.2; load type is a factor associated with the load type (0.3 is for resistive loads, 8 is for inductive loads; and 6 is for capacitive loads); and manoeuvres is a factor related to the number of manoeuvres per hour at 1;

(19)

Process

×(

× SIm

FUSE 0_Fuse

PM

where 0_CB is the basic failure rate associated with main components of a circuit breaker at 0.85; Thermal , Electrical , TCy , Mechanical , and RH are acceleration factors related to thermal, electrical, thermal cycling, mechanical and relative humidity effects, respectively. The electrical factor, Electrical , is shown by Eq. (22).

2.3.2. Failure rates of protective devices

=[

0_CB

×

1, then m = 3

(24)

with Iapplied is the applied current across the CB, and Inominal is the nominal current of the CB. It can be seen that the failure rate of CB, CB , or the electrical factor, Electrical , are related to the power loss and the system power input levels, relying on the temperature and voltage.

(20)

where IApplied is the applied current across the fuse; Ir , Fuse is the rated 5

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T.T. Pham, et al.

c) Failure rates of protective relays

TCap = Ta +

Similar to the failure rate of CB, the failure rate of relay, determined as the following:

Relay

0_Relay

×

×(

Induced ]

Thermal

×

PM

+

×

Electrical

+

+

TCy

Mechanical

+

= 0.55 ×

2.6. Reliability evaluation of bidirectional DC/AC inverters

RH )

(25)

Process

×

×

pole

EL _break

×

load type

×

manoeuvres

Considering a discharging operation mode, DC/AC power inverters are used to convert the DC voltage of the BESS into the AC voltage to be suitable with AC loads in a microgrid. For a charging operation mode, the DC/AC inverter operates as an AC/DC power rectifier in order to charge DC energy into the BESS. In general, a DC/AC inverter has no parallel redundancy, which means any failure of main components of the inverter will cause an outage of the entire inverter. Therefore, from a viewpoint of reliability evaluation, the components of an inverter are in series. In other words, the reliability model of inverter can be considered as a series network. The failure rate, INV , repair rate, µINV , and availability, AINV , of the inverter in the BESS are determined by:

× SVn × SIm

Vnominal_coil Vrated_coil

(26)

with Vrated_coil is the relay control voltage; and Vnominal_coil is the nominal operating voltage of the controlling coil of the relay. 2.4. Failure rate of diodes

INV

=

0 Diode

T

S

C

Q

µINV =

3091

=e

1 (Tdiode + 273)

(27)

E

=

1 298

(28)

(VApplied Vr , diode )2.45 if 0.3 < (VApplied Vr , diode ) < 1 0.054 if (VApplied Vr , diode )

0.3

The failure of capacitors is one of main reasons to result in the failure of power electronic inverters. In [46], the calculation of the failure rate of capacitor is as follows:

×

0_Cap

×(

Thermal Electrical

+

TCy

+

Mechanical )

×

Induced ]

×

PM

where 0_Cap is the basic failure rate associated with main components of the capacitor. Thermal Electrical is expressed by Eq. (31). In addition, according to different types of capacitors, other factors are selected from the reference [46]. Thermal Electrical

=

TE

×

1 SRef

×

VApplied Vr , Cap

3

× e

11604 × Ea ×

1 293

L

+

(

i=1

Diode Diode µi i

+

+

IGBT ) i

IGBT IGBT µi ) i 1 µ INV INV + 1 µ INV

(33)

(t ) = e

INV

(t ) dt

(34)

0

2.6.1. Power losses of IGBT and diode Power losses of an inverter are mainly caused by IGBTs and diodes. In [51,52], the power loss in an IGBT or a diode is the sum of conduction and switching losses, estimated by the following equations.

(30)

Process

CapµCap

Diode i

where the total service time of inverter includes charging and discharging times and standby times of the BESS. If a failure density function of the inverter is identified, its reliability can be easily evaluated in the system. For the reliability performance of the inverter, it is necessary to determine the correlation between the failure rate and the change in voltage and temperature. The relationship between the failure rate and the voltage fluctuation has been aforementioned, so this section will only discuss the relationship between the failure rate and the change in temperature through calculation of power losses and the thermal stress factor.

(29)

2.5. Reliability evaluation of capacitors

=[

1 INV

t

RINV

where VApplied is the applied voltage across the diode and Vr , diode is the rated withstanding voltage of the diode. The detail values of other factors can be found in the reference [49].

Cap

(

where w is a weighting factor which is the ratio of the worked time to the expected total service time of the inverter. It is noted that a standby operating condition with the zero power output state is a specific operating condition of the inverter. Cap , IGBT and Diode are failure rates of the capacitor, IGBT and diode under the operating condition, respectively. L is the total number of IGBTs or diodes of the inverter. The reliability function, RINV (t ) , of the inverter can be defined by:

The electrical stress factor [44] can be calculated by: s

L

+w×

AINV =

where 0 Diode is the base failure rate of the diode; T is the temperature factor; S is the electrical stress factor; C is the contact construction factor; Q and E are the quality and environment factors, respectively. When the junction temperature is known, the temperature factor is calculated by Eq. (28). T

Cap

=

i=1

A standard reliability model of diodes is suitable to calculate the failure rate of diodes in power electronic converters as a following equation [48]: DIODE

(32)

with Ta is the ambient temperature; c [ C/W] is the thermal resistance from the core of capacitor to environment; Rs is an equivalent series resistance; and Ir is the ripple current of the capacitor.

, is

where 0_Relay is the basic failure rate associated with main components of the relay selected at 1.1; the electrical factor of the relay is expressed by Eq. (26). Electrical

(Ir2 Rs ) 0

Relay

=[

c

IGBT IGBT P IGBT = Pcond + Psw =

± m cos 1

1 2

IGBT Vdrop

IGBT Ipeak Vdrop 8

+ fsw (Eon + Eoff )

1 TCap+ 273

Ipeak

+ RIGBT

(Ipeak )2 4

2 IGBT (Ipeak )

+R

3

VDC , applied Ipeak IGBT Vref

IGBT Iref

(35)

where is the total power loss of an IGBT; subscripts ‘cond’ and ‘sw’ IGBT denote the conduction and switching operation states of the IGBT; Vdrop is the voltage drop on the IGBT; RIGBT is the on-state resistance of the IGBT; Ipeak is the peak phase-current at the output interface of inverter IGBT IGBT calculated by Eq. (36). Vref and Iref are the reference/rated commutation voltage and current of the IGBT, respectively; VDC, applied is the DC voltage at the DC-side of the inverter; Eon and Eoff are energy losses

P IGBT

(31) where TE , SRef , Ea are selected depending on types of ceramic capacitors, aluminium capacitors, and tantalum capacitors. VApplied is the applied voltage across the capacitor while Vr , Cap is the nominal (rated) operating voltage of the capacitor. The core temperature of capacitor in a steady-state, TCap , is calculated by [50]: 6

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during the on-state and off-state of the IGBT [53]; fsw is the switching frequency of IGBT; m is the modulation index; and is the angle between the voltage and the current.

Ipeak =

2 × PtBESS 3 × VAC, L L

(36)

with is the output power of BESS under the operation time t; VAC, L L is the line-to-line output RMS voltage of the inverter which is associated with the DC bus-voltage and the voltage modulation index, m. If a typical three-phase six-switch inverter is used, VAC, L L is calculated by:

PtBESS

VAC, L

L

=

3 × VDC, applied × m

0.612 × VDC, applied × m

2 2

(37)

Fig. 2. Configuration of a battery charger/controller connected to a microgrid.

Similarly, the total power loss of a diode, P Diode , in the inverter, is determined in Eq. (38) where subscripts ‘cond’ and ‘rec’ denote the Diode conduction and recovery, respectively; Vdrop is the voltage drop on the diode; RDiode is the resistance of the diode; Erec is the reverse recovery Diode Diode energy loss of the diode [53]; and Vref and Iref are the reference/ rated commutation voltage and current of the diode, respectively. Diode Diode P Diode = Pcond + Prec =

1 2

Diode Vdrop

m cos 1

+ fsw Erec

Diode Vdrop

Ipeak 8

Ipeak

+ RDiode

+ RDiode (Ipeak

and the battery current (ibat ) flows from the inductor (LInd ) to the capacitor (C ). In the charge mode, an upper IGBT switch (Sbuck ) operates, then the bidirectional DC-DC converter acts as a buck converter, the current flows from the capacitor to the inductor to charge for a BESS. In general, the operating condition of DC-DC converter is affected by any variation in electrical parameters due to the input/output loading, transient and dynamic cases, and the change in temperature from different ambient and operating conditions. The failure rate, CONV , repair rate, µCONV , and availability, ACONV , of the battery charger/controller are determined by the following equations:

(Ipeak )2 4

)2

3

VDC , applied Ipeak Diode Vref

(38)

Diode Iref

It is noted that the signs of ± and understood as follows:

CONV

in Eqs. (35) and (38) can be

=

1

+ (c

Cap)

+

(41.1)

Inductor ]

Diode µDiode )

+ (b

IGBT µIGBT )

+ (c

CapµCap )

(41.2)

Inductor µInductor ]

ACONV =

2.6.2. Junction temperature calculation of IGBT and diode IGBTs or diodes are basically placed on a heat sink to dissipate the heat. The junction temperature Tj is the sum of the heat sink temperature, THS , and a relative temperature increase in the interface of IGBT or diode, TRT .

[(a

CONV

+

rectifier (i.e. at the charge mode of the BESS).

1 µCONV + 1 µCONV

(41.3)

CONV

RCONV (t ) = e

( CONV × t )

(41.4)

RCONV (t ) dt

MTTF =

(41.5)

0

(39)

where z is a weighting factor of the battery charger which is the ratio of the worked time to the expected total service time of the charger. It is noted that the standby operating condition with the zero power output state is a specific operating condition of the charger. Cap , IGBT , Diode and Inductor are failure rates of the capacitor, IGBT, diode and inductor under the operating condition, respectively. µCap , µIGBT , µDiode and µInductor are repair rates of the capacitor, IGBT, diode and inductor, respectively. Thea , b and c variables are the total number of diodes, IGBTs, and capacitors of the battery charger, respectively.

where,

THS = TA + n (P IGBT + P Diode ) RHS TRT = max(P IGBT RRT , P DiodeRRT )

IGBT )

+ (b

µCONV

• The upper sign is used when the reconfigurable converter works as an inverter (i.e. at the discharge mode of the BESS). • The lower sign is used when the reconfigurable converter works as a

Tj = THS + TRT

Diode )

= z [(a

(40)

where TA is the ambient temperature; n is the number of modules placed on the heat sink (e.g. it is 6 modules for a configuration of three-phase six-switch power inverter); RHS and RRT are thermal resistances from the heat sink to the ambient environment and from the junction to the interface of the IGBT or diode, respectively. In general, when the junction temperature and the applied voltage across the IGBT or the diode of the inverter are changed, their thermal stress factors will be appropriately changed such that these factors could certainly lead to an increase in the failure rates of IGBT and diode. Consequently, the inverter failure rate will be correspondingly increased.

2.7.1. Failure rate of inductors Calculation of the failure rate of inductor is as follows: Inductor

=[ ×

0_Inductor PM

×(

×

Thermal Electrical

+

TCy

+

Mechanical)

×

Induced ]

(42)

Process

where 0_Inductor is the basic failure rate associated with main components of the inductor; Thermal Electrical is expressed by Eq. (43). In addition, according to different types of inductors, other factors are selected from the reference [46].

2.7. Reliability evaluation of DC/DC converters or battery controllers/ chargers Fig. 2 shows a basic configuration of battery charger/controller that can be mostly called a bidirectional DC-DC converter. It mainly consists of two IGBT switches, an inductor, diodes, and capacitors. In the discharge mode, a lower IGBT switch (Sboost ) operates, the converter boosts the voltage of battery (v BESS ) to the voltage of common DC-bus (v DC bus )

Thermal Electrical

=

TE

× e

11604 × Ea ×

1 293

1 (T board ambient + T + 273)

(43)

where TE , Ea and T are selected depending on types of inductors (e.g. low/high current wire-wound inductors, multi-layer inductors, low/ 7

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high power transformers); is a component temperature increase relative to the ambient temperature (°C). The junction temperature (Tj ) of the inductor is the sum of the board-to-ambient temperature (Tboard ambient ) and a temperature increase of T .

2.7.3. Junction temperature calculation of IGBT, diode, and inductor in the battery charger The junction temperature Tj is the sum of the heat sink temperature, THS , and a relative temperature increase in the interface of IGBT, inductor or diode, TRT .

2.7.2. Power losses of IGBT, inductor, and diode in the battery charger The total power loss of an IGBT or a diode is the sum of conduction and switching losses, estimated by the following equations.

in case,

• For the operation mode of DC-DC boost converter (i.e. the discharging

THS = TA + (aP Diode + bP IGBT + P Ind ) RHS TRT = max(P IGBT RRT , P DiodeRRT , P IndRRT )

mode):

1

fsw (Eon + Eoff )

VDC, applied Is, peak IGBT Vref

IGBT Iref

(44) where D is a duty cycle; VT is the on-state drain-source voltage of the switch, usually selected at 0.5 V; Ron is the drain-source on-state resistance of the switch; Is, peak is the peak input current of DC-DC boost converter and VDC, applied is the applied voltage across the IGBT switch. Diode Diode P Diode = Pcond + Prec = (1

D)(VF + RDiodeId, peak ) Id, peak +

1

3. Discrete probability distribution of failure rates in the ABESS

fsw Erec

VDC, applied Id, peak Diode Vref

Diode Iref

Considering a conventional reliability evaluation method of the ABESS, the failure rate of ABESS is a basic function of the worked time. However, the failure rate of the ABESS is also a function of the appliedvoltage and temperature. According to discharging and charging states, voltage-fluctuation and power-loss dependent failure rates (VF-PL DFR) of the ABESS will be analyzed. Under randomly dynamic operation scenarios of the ABESS in microgrids, voltage, current, power/energy loss, and the charge/discharge duration of the ABESS will be different. This can lead to a corresponding change in failure rates of the ABESS. Measurement of electrical parameters of the ABESS will be done in randomly dynamic operation scenarios such that the failure rates can be properly calculated and aggregated into a discrete probability distribution. A K-mean clustering technique is used to eliminate outliers and divide data points into several levelized groups [51]. The calculated values of failure rate of the ABESS are divided into K levels. K can be adjusted depending on the required reliability analysis. Then, N data points of the failure rate can be clustered into K levels based on the following steps:

(45)

where VF is the forward voltage of the diode; RDiode is the on-state resistance of the diode; Id, peak is the peak current across the diode

(I

d, peak

=

V BESS Rload (1 D )2

+

the inductance.

V BESSD 2fsw Lind

) with R

load

the load resistance, and Lind is

P Ind = RindIL2, peak

(46)

where P Ind is the power loss of inductor; Rind is the equivalent resistance of the inductor; and IL, peak is the peak current across the inductor during the operation modes of boost converter.

• For the operation mode of DC-DC buck converter (i.e. the charging mode):

IGBT IGBT P IGBT = Pcond + Psw = D (VT + Ron Is 1

+ fsw (Eon +

buck , peak ) Is buck , peak

VDC , applied Is buck, peak Eoff ) V IGBT IGBT Iref ref

(47)

i) Arbitrarily select data points to each cluster, with K initial clusters, we have = { 1, 2, , K } ; determine the initial cluster mean µi , where i corresponds to a cluster i , i = 1, 2, , K ; ii) Calculate the distance dji from each data point Xj (j = 1, 2, , N ) to the ith cluster mean µi

where Is buck, peak is the peak current flowing through the IGBT switch of a buck converter;

Is

buck , peak

=

(V DC

bus

V BESS ) D (48)

fsw Lind

where respectively;

V DC bus and

V BESS

are the voltages of common DC-bus and BESS,

Diode Diode P Diode = Pcond + Prec = (1 1

+ fsw Erec

D )(VF + RDiodeId

dji = |Xj

Diode Iref

(49)

µi =

where Id buck, peak is the peak current flowing through the diode of a buck converter;

Id

buck , peak

= V BESS

1 (1 D ) + BESS 2fsw Lind Requ

buck, peak

1 Ni

Xj Xj

with i = 1, 2, …, K

(55)

i

where N i is the number of data points in the

ith

cluster. (55)

iv) Repeat steps ii) and iii) until each and every µi remains unchanged or lower than a pre-defined error between two iterations; v) The converged µi is the ith cluster mean with a discrete probability equaling to N i N . Based on the discrete probability distribution of failure rate, common failure density functions, e.g. normal, exponential, Weibull, Rayleigh, lognormal distributions, could be properly selected for the failure rates of components in the ABESS during the reliability assessment.

(50)

BESS where Requ is the equivalent resistance of the BESS.

P Ind = RindIL2

(54)

µi |

iii) Assign each data point Xj to the nearest cluster with minimum distance for j = 1, 2, , N ; then recalculate the mean of K clusters by:

buck , peak ) Id buck , peak

VDC , applied Id buck, peak Diode Vref

(53)

where TA is the ambient temperature; RHS and RRT are thermal resistances from the heat sink to the ambient environment and from the junction to the interface of the IGBT, inductor, or diode, respectively. In general, when the junction temperature and the applied voltage across the IGBT, inductor, or diode of the bidirectional DC-DC converter are changed, their thermal stress factors will be appropriately changed such that these thermal factors could lead to an increase in failure rates of IGBT, inductor, and diode. Consequently, the failure rate of the bidirectional DC-DC converter will be correspondingly increased.

IGBT IGBT P IGBT = Pcond + Psw

= D (VT + Ron Is, peak ) Is, peak +

(52)

Tj = THS + TRT

(51)

where IL buck, peak is the peak current across the inductor during the operation modes of buck converter. 8

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Fig. 3. Diagram of an ABESS in a local energy community with multiple microgrids.

such as: protection of DC/DC converters and battery arrays. Circuit breakers are used to protect AC sides of the ABESS such as: protection of DC/AC inverters and AC loads. The AC side of the ABESS is considered as a three-phase power system. In general, a two-step approach is used for reliability evaluation of the entire ABESS. First, a reliability model of each component in the ABESS is analyzed and parameterized as presented in Section 2. Then, the system-level reliability is evaluated by Markov-based reliability models. The advantage of Markov method is to specify each component′s failure rate of the ABESS under dynamic behaviors. As seen in Fig. 3, there are two DC and AC common-buses in the ABESS. Therefore, the system-level reliability will be evaluated

4. Reliability analysis of the entire ABESS in microgrids An overall diagram of the ABESS in the microgrid is studied before doing the reliability assessment of the ABESS. As shown in Fig. 3, an ABESS includes many battery arrays connected in parallel. Each battery array is connected to a bidirectional DC-DC converter to control the charging and discharging process of the battery. The outputs of DC-DC converters are connected to a DC common-bus to supply DC loads and share the DC power among them. DC/AC inverters are connected to the DC common-bus to convert the DC power into the AC power for supplying AC loads and connecting to a local energy community (LEC) with multiple microgrids. DC fuses are used to protect DC sides of the ABESS 9

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T.T. Pham, et al.

Fig. 4. A reliability evaluation methodology of the ABESS.

according to two sub-systems that are connected in series. Specifically, a DC sub-system consists of battery arrays, DC fuses, and bidirectional DC-DC converters. An AC sub-system contains DC fuses, bidirectional DC/AC inverters, and AC circuit breakers. The Markov-based reliability models are developed for these two sub-systems, as presented in the following sub-sections and referred to Fig. 4.

and move from the state (i) to the state (i + nP ) with a transition rate of (NBA z ) CONV [i] where z is the number of failed battery arrays at the state (i); and CONV [i] is the failure rate of the (z + 1) th DC/DC converter. It is noted that all battery modules in the ABESS are assumed to operate at the same capacity. After the failure of a string of battery modules, all DC/DC converters are assumed to change equally in order to significantly reduce the number of states and transitions required in the Markov model. A failure of DC fuses at the inputs and outputs of DC/DC converters can also result in the ABESS to lose nP strings and move from the state (i) to the state (i + nP ) with a transition rate of (NBA x ) FI [i] where x is the number of failed input fuse-pairs at the state (i) and FI [i] is the failure rate of the (x + 1) th input fuse-pair of the converters; or with a transition rate of (NBA y ) FO [i] where y is the number of failed output fuse-pairs at the state (i) and FO [i] is the failure rate of the (y + 1) th output DC fuse-pair of the converters. According to Fig. 5, the DC sub-system′s operating behavior is described as the following. At timet =0, the ABESS is assumed to be in state 0, i.e., P0 (0) = 1 and Pi (0) = 0 for i > 0 .

4.1. Reliability of a DC sub-system in the ABESS Failure of a single battery module leads to isolation of the whole string with series-connected battery modules where contains the failed battery module, as referred to Fig. 3 [54]. A battery array continues to operate normally as long as the number of parallel strings in the battery array is available. The total number of parallel strings is calculated by Eq. (56) where NBA is the number of battery arrays in the ABESS; np is the number of parallel strings in a battery array, and re is the energy redundancy ratio.

Total number of parallel strings = NBA np re

with

re

1

(56)

dP0 = dt

A Markov state transition diagram for the DC sub-system of the ABESS is presented in Fig. 5. The total number of states is the total number of parallel strings of the ABESS. Each state has four variables, specifically including the number of failed parallel strings, the number of failed DC/DC converters, the number of failed DC fuses at the converter input and output. Pi is the probability of the DC sub-system being a steady state where i parallel strings have been failed. The failure rate for transiting from the state (i) to the state (i + 1) is (NBA np i ) R [i], where R [i] is the failure rate of the (i + 1) th parallel string. Failure of a bidirectional DC/DC converter will cause the system to lose nP strings

dPi dt

(NBA

CONV [0]

+ NBA

FI [0]

+ NBA

= (NBA

z + 1)

CONV [i np] Pi np

+ (NBA

y + 1)

FO [i np] Pi np

[(NBA + (NBA nP

z)

CONV [i] + (NBA

i)

FO [0]

+ NBA nP

R [0] ) P0

+ (NBA

x + 1)

FI [i np] Pi np

+ (NBA nP

i + 1)

R [i 1] Pi 1

x)

FI [i] + (NBA

y)

(57)

FO [i]

R [i] ] Pi

with i = 1. ..NBA np re

(58)

The mean time to failure (MTTFDC-sub-system-ABESS) of the DC sub10

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Fig. 5. Markov state transition diagram for a DC sub-system of the ABESS.

system can be calculated using the Laplace transformation of Pi , Pi [55].

the number of failed CBs. The total number of states is the total number of parallel inverters in the ABESS, NINV rP , where NINV is the total number of DC/AC inverters; rP is the power redundancy ratio, rP = Prequired NINV PINV 1. Prequired is the rated power required from the ABESS and PINV is the nominal power of each inverter. A failure of DC fuses at the input of inverters can also result in the AC sub-system to move from the state (j) to the state ( j + 1) with a transition rate of (NINV j ) FI INV [j] where j is the number of failed parallel inverters and also the number of failed input fuse-pairs at the state (j) and FI INV [j] is the failure rate of the (j + 1) th input fuse-pair of the inverters. Similarly, the failure of AC circuit breakers at the output of inverters can cause the AC sub-system to move from the state ( j ) to the state ( j + 1) with a transition rate of (NINV j ) CB INV [j] where j is the number of failed CBs at the state (j) and CB INV [j] is the failure rate of the (j + 1) th AC circuit breaker of the inverters. According to Fig. 6, the AC sub-system’s operating behavior is described as the following. At timet =0, the sub-system is assumed to be in state 0, i.e., P0 (0) = 1 and Pj (0) = 0 for j > 0 .

NBA np re

R (t ) =

Pi

(59)

i=1 NBA np re

MTTFDC

sub system ABESS

=

Pi (0) = i=1

R (t ) e 0

st dt

(60)

4.2. Reliability of an AC sub-system in the ABESS The DC/AC power inverters are used to connect between a DC subsystem and an AC sub-system in the ABESS. These inverters are connected in parallel. Pj is the probability of the AC sub-system being a steady state where j parallel inverters have failed. The failure rate for transiting from the state ( j ) to the state ( j + 1) is (NINV j ) INV [j], where INV [j] is the failure rate of the (j + 1) th parallel inverter. A Markov state transition diagram for the AC sub-system is presented in Fig. 6. Each operation state has three variables, namely, the number of failed parallel inverters, the number of failed input DC-fuse-pairs, and

Fig. 6. Markov state transition diagram for an AC sub-system of the ABESS. 11

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T.T. Pham, et al.

Fig. 7. Markov state transition diagram of the entire ABESS.

dP0 = dt dPj dt

NINV

INV [0] P0

= (NINV

j + 1)

the ABESS. Therefore, the failure and repair rates for each sub-system should be re-calculated. In particular, voltage-fluctuation and powerloss dependent failure rates (VF-PL DFR) of each sub-system will be determined for the reliability evaluation. It is noted that the overall failure rate of each subsystem of the ABESS is a summation of the usedtime-dependent failure rate and the voltage-fluctuation and power-loss dependent failure rates. As seen in Fig. 7, the ABESS’s operating behavior is described as the following. At time t =0, the ABESS is assumed to be in state 0, i.e., P00 (0) = 1 and Pij (0) = 0 for i > 0 and j > 0 . DC sub system ABESS [i] is the failure rate of DC sub-system with i failed parallel strings, while DC sub system ABESS [j] is the failure rate of AC sub-system with j failed parallel inverters. The total number of states is the total number of (re NBA nP )(NINV rP ) in the Markov diagram.

(61) INV [j 1] Pj 1

(NINV

j)

INV [j] Pj

with j (62)

= 1. ..NINV rp

The mean time to failure (MTTFAC-sub-system-ABESS) of the AC subsystem can be calculated using the Laplace transformation of Pj , P j [55]. NINV rp

R (t ) =

Pj

(63)

j=1 NINV rp

MTTFAC

sub system ABESS

=

P j (0) = j=1

R (t ) e

st dt

0

dP00 = dt

(64)

4.3. Reliability of the whole ABESS

dPij dt

=

DC sub system ABESS [i 1] DC sub system

+

+

AC sub system ABESS [1] ) P00

(67)

AC sub system ABESS [j 1] ) P(i 1)(j 1)

ABESS [i] +

AC sub system ABESS [j] ) Pij

(68) Using a Laplace transformation of Pij, Pij , the mean time to failure of the whole ABESS is: re NBA nP NINV rP

MTTFABESS =

Pij (0) = i=1

j=1

1 ABESS

(69)

DC sub system ABESS DC sub system ABESS

( µABESS =

DC sub system ABESS [1]

(

A Markov state transition diagram for reliability assessment of the entire ABESS is shown in Fig. 7. Pij represents the probability of ABESS in a state where i parallel strings and j parallel inverters have been failed. Failure and repair rates for each sub-system is symbolled as and AC sub system ABESS DC sub system ABESS , µDC sub system ABESS , µAC sub system ABESS . The failure and repair rates of the whole ABESS can be estimated by: ABESS

=(

(

+

DC sub system ABESS

(µDC + +

+

sub system ABESS .

DC sub system ABESS .

AC sub system ABESS

(65)

5. Simulation on dynamic operation cases of a microgrid with the ABESS and PV system

AC sub system ABESS )

µAC

Reliability analysis of the ABESS is performed by a microgrid simulation model with the ABESS and the PV system, as shown in Fig. 8. The PV system consists of a total of 50 PV strings in parallel, with 22 PV modules in series of a string and 36 PV cells in series of a module. The other parameters of the PV system are shown in Appendix A. The ABESS has a nominal voltage of 500VDC and a rated capacity of 6.58kAh. The nominal charge/discharge currents of ABESS and an initial state of charge (SOC) are changed according to differently dynamic operation cases. An overall design of the ABESS is shown in Table 1. The ABESS

sub system ABESS )

AC sub system ABESS

DC sub system ABESS . AC sub system ABESS .

µAC

µDC

sub system ABESS sub system ABESS

(66)

According to the number of failed parallel strings and inverters, the probability of ABESS will be different. When one or some of parallel strings/inverters are failed, it appears dynamic operation situations of 12

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T.T. Pham, et al.

Fig. 8. Simulation model of the ABESS combined with a PV system in microgrids.

uses 5% additional battery modules to compensate for loss in the accessible capacity due to lack of active balancing. An energy redundancy ratio, re , is selected at 0.9 and a power redundancy ratio, rP , is selected at 0.85. A bidirectional DC/DC converter has the nominal power of 25 kW, the rated input voltage of 500VDC and the rated output voltage of 750 VDC. The other parameters of the converter such as efficiency, switching frequency, voltage and current ripples are shown in Appendix B. DC/AC inverters have the nominal power of 25 kW, the rated input DC voltage of 750 VDC, and the rated output AC voltage of 220/380VAC. The remaining parameters of the inverters, e.g. efficiency, switching frequency, total harmonic distortion are mentioned in Appendix C. On the other hand, protective devices in the ABESS such as DC fuses and AC circuit breakers are properly selected according to the rated parameters of DC/DC converters and DC/AC inverters. Table 2 shows main parameters for reliability evaluation of IGBT switching devices, protective devices, diodes, capacitor, inductor, and PV module. These parameters are used to calculate voltage-fluctuation

and power-loss depending failure rates of critical components in the ABESS. Dynamic operation simulation of an ABESS aims to determine voltage-fluctuation and power-loss dependent failure rates (VF-PL DFR) of main components in the whole ABESS. These failure rates are incorporated in reliability evaluation of the entire ABESS. With respect to dynamic operation conditions, the sudden change in load power, the intermittent and unstable operation of PV sources, and two grid-connected and islanded operation modes of the microgrid are simulated by PSCAD software. A topology of battery arrays is assumed to be fixed during the simulation. According to different operation scenarios, the failure rates of components in the ABESS will be correspondingly changed. Table 3 and Table 4 show dynamic simulation cases of the ABESS in the microgrid with the PV system. The total simulation time is 50 s. A random increase or decrease in load power of the microgrid is simulated from the 5-th second to the 13-th second, as referred to Fig. 9. In addition, Fig. 10 shows a sudden change in PV source power based

Table 1 Design of the ABESS. Main parameters

Description

Number of battery arrays Number of battery strings in an array Number of battery modules in a string Number of battery cells in a module Number of bidirectional DC-DC converters Number of DC fuses at the inputs of converters Number of DC fuses at the outputs of converters Number of DC fuses at the inputs of inverters Number of AC circuit breakers (CBs) Number of DC/AC inverters The used-time-dependent failure rates (failures/year) and repair rates + Battery module + Converter + Inverter: + DC fuse + AC circuit breaker + IGBT/MOSFET + Diode + Capacitor + Inductor

10 battery arrays/system 9 strings/array 14 modules/string 36 cells/module 10 converters 20 fuses 20 fuses 20 fuses 10 circuit breakers 10 inverters 0.0312 0.1250 0.1430 0.0500 0.1000 0.3000 0.1000 0.4000 0.4000

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failures/year failures/year failures/year failures/year failures/year failures/year failures/year failures/year failures/year

10 26 21 52 10 17 26 26 26

repairs/year repairs/year repairs/year repairs/year repairs/year repairs/year repairs/year repairs/year repairs/year

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Table 2 Critical parameters for reliability analysis of the base cases.

Table 3 Dynamic simulation cases of the ABESS starting at a grid-connected operation mode1. (a) The on-grid operation mode of the ABESS: From the starting time to the 20th second Change in load power (kW):

At the 5th second 75 kW At the 10th second 200 kW

At the 6th second 100 kW At the 11th second 150 kW Change in solar irradiation At the 14th second (W/m2): 800 PV operation status: From the 8th to 10th second OFF (b) The off-grid operation mode of the ABESS: From the 20th second to the 35th second

At the 7th second 125 kW At the 12th second 100 kW At the 15th second 900

At the 8th second At the 9th second 150 kW 175 kW At the 13th second 50 kW At the 16th second At the 17th second 1000 800 From the 17th to 19th second OFF

Change in load power (kW):

At the 21st second 75 kW At the 26th second 200 kW

At the 23th second 125 kW At the 28th second 100 kW At the 31st second 900

At the 24th second 150 kW At the 29th second 50 kW At the 32nd second 1000

At the 22nd second 100 kW At the 27th second 150 kW Change in solar irradiation At the 30th second (W/m2): 800 (c) The on-grid operation mode of the ABESS: From the 35th second to the ending time 1

The initial state of charge (SOC) is 50%. 14

At the 25th second 175 kW At the 33th second 800

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Table 4 Dynamic simulation cases of the ABESS starting at an islanded operation mode2. (a) The off-grid operation mode of the ABESS: From the starting time to the 20th second Change in load power (kW):

At the 5th second 75 kW At the 10th second 200 kW

At the 6th second 100 kW At the 11th second 150 kW Change in solar irradiation At the 14th second (W/m2): 800 Operation status of PV system: From the 8th to 10th second OFF (b) The on-grid operation mode of the ABESS: From the 20th second to the 35th second

At the 7th second 125 kW At the 12th second 100 kW At the 15th second 900

At the 8th second At the 9th second 150 kW 175 kW At the 13th second 50 kW At the 16th second At the 17th second 1000 800 From the 17th to 19th second OFF

Change in load power (kW):

At the 21st second 75 kW At the 26th second 200 kW

At the 23th second 125 kW At the 28th second 100 kW At the 31st second 900

At the 24th second 150 kW At the 29th second 50 kW At the 32nd second 1000

At the 22nd second 100 kW At the 27th second 150 kW Change in solar irradiation At the 30th second (W/m2): 800 (c) The off-grid operation mode of the ABESS: From the 35th second to the ending time 2

At the 25th second 175 kW At the 33th second 800

The initial state of charge (SOC) is 80%.

A summation of the voltage–fluctuation and power–loss dependent failure rates (VF-PL DFR) and the used-time-depending failure rates (TPFR) for main components of the ABESS is calculated to assess the reliability of the entire ABESS. 6.1. Reliability results of battery modules Fig. 11 shows a failure rate of battery module depending on charging/discharging current values and the applied voltage. The failure rate is approximate at 140 failures/106 h. In Fig. 11a, when the charging/discharging currents of battery module are in a proper range (max 200A for the discharging and max 100A for the charging), the failure rate is insignificantly changed. The failure rate of BM is zero when the

Fig. 9. Change in the load power for surveying dynamic characteristics of the ABESS.

Fig. 10. Change in the PV-source power for surveying dynamic characteristics of the ABESS.

on the solar irradiation change; and the intermittent operation of this PV source from the 8-th second to the 20-th second. The simulation time from the beginning to the 20-th second is for the on-grid operation mode of the ABESS, while the off-grid operation mode of the ABESS is from the 20-th second to the 35-th second. Grid re-connection of the ABESS is performed right after the 35-th second. Noted that the change in load power and PV-source power is also simulated during the off-grid operation mode of the ABESS. 6. Reliability testing results This section presents reliability testing results of all critical components of an ABESS as well as the whole ABESS under dynamic operation conditions of the microgrid where contains the ABESS and PV system. Failure rates of battery modules, switching and protective devices, capacitors, DC/AC inverters, and battery controllers/chargers are also determined over randomly dynamic operation cases of the ABESS.

Fig. 11. Failure rate of the BM versus charging/discharging current values and the voltage value. 15

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Fig. 13. Current-depending failure rate of the DC fuse.

current of 1kA. It can be obviously seen that when the DC current is lower than 0.65kA, there are few outliers of the failure rate of DC fuse as shown in Fig. 13. It also means that the operation reliability of DC fuses is very high if the ABESS is being at the normal operation mode without dynamic situations. At this case, the usedtime-dependent failure rate of the DC fuse is about 0.0500 failures/ year. (ii) When the applied current of DC fuses is in a range of 0.65kA to 0.95kA, the current-depending failure rate of the DC fuse is about 5.9 failures/106 h. Around a threshold current of 1kA, the currentdepending failure rate of the DC fuse is the highest at 6.6 failures/ 106 h. Most calculation results of the failure rate of DC fuses with regard to randomly dynamic operation cases of the ABESS are converged to a place where the applied current of DC fuse fluctuates at the protective threshold of 1kA.

Fig. 12. Voltage-depending failure rate of the IGBT switching device.

BM operates at a standby mode. In Fig. 11b, the failure rate of BM only slightly changes around 140 failures/106 h when the voltage is changed in an allowable limit.

The AC circuit breakers are used to protect DC/AC inverters and AC loads in the ABESS. The current-depending failure rate of the AC circuit breaker mostly remains at 4.75 failures/106 h when the applied current of CBs is lower than 0.65kA as presented in Fig. 14. At a range of the applied current from 0.65kA to 1.3kA, the failure rate of CBs is approximately distributed by an exponential function. The average current-depending failure rate of CBs is 5 failures/106 h.

6.2. Reliability results of switching and protective devices Reliability results of a IGBT switching device are illustrated in Fig. 12. In Fig. 12a, the voltage-dependent failure rate (VDFR) of the IGBT remains unchanged at 6.2 failures/106 h when the applied voltage across it is lower than 5 kV. However, when the applied voltage gradually increases to a nominal maximum value of 10 kV, the VDFR of the IGBT rises very quick up to 8.3 failures/106 h. If the withstanding voltage of IGBT is higher than 10 kV, the reliability result of the IGBT will be inappreciable because the IGBT has been damaged. The voltage-fluctuation and power-loss depending failure rate of the IGBT is presented in Fig. 12b. It can be observed from Fig. 12b that:

6.3. Reliability results of inductors and capacitors Reliability results of inductors and capacitors under dynamic operation conditions of the ABESS are presented in Figs. 15 and 16, respectively. It can be seen from Fig. 15 that: (i) The VDFR of inductors is insignificant when the applied voltage is lower than 0.32 kV. There are few outliers of the VDFR as observed in Fig. 15. (ii) The VDFR of inductors is mostly remained at 22 failures/106 h when the applied voltage is at between 0.32 kV and 0.5 kV. (iii) It is noted that the inductors are used for a structure of DC/DC converters. The failure rate of inductors depends on both the

(i) The voltage-fluctuation and power-loss depending failure rate (VFPL DFR) is very high in comparison to the voltage-depending failure rate. Specifically, the VF-PL DFR has a linearly approximate increase from 6.2 failures/106 h to about 350 failures/106 h when the applied voltage of IGBT increases from 0 V to 7 kV in correspondence. A main reason is that power loss of the IGBT is very high due to a significant increase of the operating voltage, which also leads to a sudden change in the failure rate of the IGBT. (ii) The IGBT is still able to work during the applied voltage change of the IGBT if being lower than a maximum value of 10 kV. DC fuses are used to protect battery arrays, DC/DC converters, and DC/AC inverters in the ABESS. An increase in the current flowing through the DC fuses can cause a higher current-dependent failure rate. Fig. 13 illustrates reliability results of the DC fuse. It can be concluded that: (i) The failure rate of DC fuse is not appreciable when the operation current flowing through it is lower than a protective threshold

Fig. 14. Current-depending failure rate of the AC circuit breaker. 16

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Fig. 17. Voltage and power-loss depending failure rate of diodes under dynamic operation.

Fig. 15. Voltage-depending failure rate of the inductor under dynamic operation.

affecting the VF-PL DFR of diodes. In general, it can be difficult to determine a failure density function of the diode. As seen in Fig. 17, a mean value of the VF-PL DFR is approximately 0.07 failures/ 106 h in case of the applied voltage above 5 kV. 6.5. Reliability results of DC/AC inverters Fig. 18 illustrates reliability results of the DC/AC inverter under differently dynamic conditions. A weighting factor ω is the ratio of the worked time to the expected total service time of the inverter, which has considered dynamic cases during the working time. In Fig. 18a, the failure rate of inverter is about 50 failures/106 h when the weighting factor is lower than 0.2. Due to the large effect of dynamic operation, the failure rate doubles when the inverter is at 20–30% life-cycle. There are many data points of the failure rate converged to this life-time period. When the life-time of inverter is above 60%, the data distribution of failure rate is mostly discrete with a mean value of approximately 300 failures/106 h. In Fig. 18b, the repair rate of inverters is distributed by an exponential function. When the life-time of inverter increases above 50%, its operation reliability decreases very quick such that the repair rate of inverter is low at below 50 repairs/106 h. Fig. 18c shows the availability of inverters as a function of the weighting factor. The inverter in the ABESS is vulnerable to voltage variations of dynamic cases. Data points of the availability are discrete in a range of 0.96–0.997 for the 5–12%, 17–27%, and above 55% life-time periods. Otherwise, the inverter availability is relatively remained above 0.99 for a 30–55% life-time period. Finally, Fig. 18d shows the reliability of inverter during the life-time cycle. The reliability strongly decreases when dynamic operation cases of the ABESS occur in the 5–12%, 17–27%, and above 55% life-time periods. It is worth noting that the reliability of inverter significantly reduces from 70% to 20% if dynamic situations occur randomly after half of the expected total service time. In addition, there are also several data outliers of the reliability of inverter during the calculation process due to transient phenomenon at the beginning time of dynamic operation.

Fig. 16. Voltage-depending failure rate of the capacitor under dynamic operation.

operating voltage and control strategies of DC/DC converters. This is a main reason to explain why the VDFR of inductors decreases to 7 failures/106 h while the applied voltage increases above 0.5 kV. In summary, the control of switching period and duty cycle in the DC/DC converter, along with the voltage fluctuation from dynamic conditions, strongly impact on the VDFR of inductors. Moreover, it can be concluded from Fig. 16 that: (i) The VDFR of capacitors increases very quick when their applied voltage approaches to the rated value of 1 kV. At the voltage 0.95 kV, the VDFR can get 200 failures/106 h. (ii) The VDFR of capacitors is also fluctuated at 6.5 failures/106 h when the applied voltage is lower than the operating voltage of ABESS at 0.5 kV. 6.4. Reliability results of diodes

6.6. Reliability results of DC/DC converters or battery controllers/chargers

Under differently dynamic conditions of the microgrid, the reliability result of diodes is shown in Fig. 17. The following observations can be made from Fig. 17:

Reliability results of DC/DC converters over dynamic operation conditions are presented in Fig. 19. A weighting factor z is the ratio of the worked time to the expected total service time of the converter, which has considered dynamic operation cases during the working time. In Fig. 19a, the failure rate of converter varies on a reliable range of 0–100 failures/106 h when its working time is lower than 60% of the life cycle. Above 65% of the expected total service time, the failure rate of the converter can exceed 100 failures/106 h. However, there are many data outliers in that service time such that the failure rate of the converter can get about 500 failures/106 h. It can be seen from Fig. 19b that: (i) the repair rate of converters quickly decreases from 800 repairs/106 h to 50 repairs/106 h followed by an exponential function when the worked time of the converter is

(i) Diodes are used for the configurations of DC/DC converters and DC/AC inverters. The failure rate of diodes depends on the applied voltage and control strategy of converters/inverters. The voltagefluctuation and power-loss depending failure rate (VF-PL DFR) of diodes is stable at about 0.02 failures/106 h when the applied voltage is below 5 kV. (ii) When the applied voltage of diodes is higher than 5 kV, the distribution of failure rates is discrete. This can be explained by different control methods (e.g. active and reactive power (P/Q) control, voltage and frequency (V/f) control) of converters/inverters 17

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Fig. 18. Reliability results of the inverter under dynamic operation, (a) Failure rate versus the weighting factor z; and (b) Repair rate versus the weighting factor z.

lower than 50% of the expected total service time; and (ii) the repair rate is very low at 25–50 repairs/106 h when the working time of the converter is larger than half of the life cycle. The availability of DC-DC converters is indicated in Fig. 19c. Similar to the availability of inverters, the availability of DC-DC converter of an ABESS is certainly vulnerable to the voltage fluctuations of dynamic cases. Data points of the availability are discrete in a range of 0.97–0.995 for the 5–12%, 17–27%, and above 55% life-time periods. Otherwise, the converter availability is stably remained above 0.99 for a 30–55% life-time period. On the other hand, Fig. 19d shows the reliability of DC-DC converter as a function of the weighting factor of the converter. The reliability

Fig. 19. Reliability results of the converter under dynamic operation, (a) the failure rate and (b) the repair rate versus the weighting factor z, and (c) the availability of DC/DC converter.

decreases remarkably when dynamic cases of the ABESS occur in the 5–12%, 17–27%, and above 55% life-time periods. The reliability of DC-DC converter reduces from 80% to 40% if dynamic situations occur randomly after half of the expected total service time. Several data outliers of the reliability are appeared during the calculation process 18

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Fig. 21. Reliability results of the entire ABESS when only considering AC loads; (a) the failure rate, (b) the reliability, and (c) the MTTF versus the weighting factors of the ABESS.

Fig. 20. Reliability results of the entire ABESS when considering both DC and AC loads; (a) the failure rate, (b) the reliability, and (c) the MTTF versus the weighting factor of the ABESS.

operation cases. However, it can be observed that the highest failure rate of the ABESS in Fig. 20a gets 750 failures/106 h after 65% of the expected total service time. Fig. 20b indicates the reliability of the ABESS as a function of the weighting factor z. The operation reliability of ABESS is significantly reduced in the life-time periods of 20–35%, 50–60% and above 65%. Noted that the reliability cannot be appreciable if large fluctuations of the applied voltage occur at the wear-out period of the ABESS (i.e. a period of after 75% of the expected total service time). Fig. 20c shows the mean time to failure (MTTF) of the ABESS which is calculated by the Markov reliability model, as referred to Section 4.1. The MTTF varies on a range of 12–57 years according to the component failure rate and the weighting factor of the ABESS. Moreover, the MTTF reduces very quickly with respect to dynamic operation cases of the ABESS, which is much sensitive to the applied voltage and the power-loss. Fig. 21 illustrates reliability results of the entire ABESS in a microgrid under dynamic operation when only considering AC loads. In

due to transient phenomenon at the beginning time of dynamic operation. 6.7. Reliability results of the entire ABESS in microgrids under dynamic operation As presented in Section 4.3, the failure rate of ABESS is assessed by two cases, including (i) both DC and AC loads; and (ii) only AC loads. Fig. 20 shows reliability results of the entire ABESS in the microgrid under dynamic operation when considering both DC and AC loads. In Fig. 20a, the failure rate of ABESS fluctuates in a wide range of 150–300 failures/106 h because the dynamic operation is randomly occurred during the working time of the ABESS in the microgrid. There are the noticeable fluctuations of failure rate in the life-time periods of 20–35%, 50–60% and above 65%. Data points of the ABESS failure rate are discretely distributed in these periods. As a result, it can be difficult to predict exactly the failure rate of ABESS under differently dynamic 19

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Fig. 21a, the failure rate of ABESS fluctuates in a wide range of 200–600 failures/106 h. Data points of the ABESS failure rate are discretely distributed in the life-time periods of 20–35%, 50–60% and above 65%. The highest failure rate of the ABESS gets 2500 failures/106 h after 65% of the expected total service time. Without dynamic situations, the failure rate of ABESS mostly stabilizes at 250 failures/106 h. Fig. 21b indicates the reliability of the ABESS as a function of the weighting factors z and w. The operation reliability of ABESS is significantly reduced in the life-time period of above 65%. Noted that the reliability cannot be appreciable if high fluctuations of the applied voltage occur at the wear-out period. Fig. 21c shows the mean time to failure of the ABESS which is calculated by the Markov reliability model, as referred to Section 4.2. The MTTF varies on a range of 4–50 years according to the component failure rate and the weighting factors of the ABESS. The MTTF reduces very quickly to 5 years with respect to dynamic operation cases happening at the life-time period of above 65%.

7. Conclusion For an aggregate battery energy storage system in the microgrid under dynamic operation conditions, a two-step reliability evaluation method based on Markov models has been presented in this paper. Reliability models of main components in the ABESS have been analyzed and parameterized depending on differently dynamic behaviors. Then, the reliability of the entire ABESS has been evaluated according to two sub-systems, mainly a DC sub-system for DC loads and an AC sub-system for AC loads. Reliability analysis of the ABESS has been implemented in a microgrid with PV generation systems. Randomly dynamic operation scenarios of the ABESS and the PV system in the microgrid have been designed and simulated by PSCAD software. Reliability results of the ABESS have illustrated that: i) Besides the used-time-dependent failure rates, voltage-fluctuation or power-loss dependent failure rates of main components (including DC/DC converters, DC/AC inverters, protective and switching devices, battery modules, and battery charger/controller) have a significant effect to a decrease in the operation reliability and availability of the ABESS. The VDFR and VD-PL DFR are dominant by differently dynamic operation conditions of the ABESS. ii) When dynamic cases of the ABESS are randomly occurred in the period of above 65% of the expected total service time, it can be seen that the failure rate increases very fast; the repair rate and the MTTF strongly decrease; and the reliability may not be appreciable at the wear-out period of the ABESS. iii) The MTTF which reduces very quickly with respect to dynamic operation cases, is much sensitive to the applied voltage stress, temperature, and power-loss. iv) The reliability of ABESS can be improved by reducing dynamic operation situations where can lead to a high increase in the applied voltage, temperature, and power-loss of the main components in the ABESS. v) A clustering technique to the discrete probability distribution model is effectively applied to data points of failure rates of main components in the ABESS.

6.8. Results of the proposed Markov-based method compared to the other existing methods In this section, numerical simulation results of the proposed Markov-based reliability evaluation method for an aggregate battery energy storage system in the microgrid under dynamic operation conditions have been briefly compared to that of the other existing methods. Specifically, reliability evaluation methodologies, failure rates, and mean times to failure of the ABESS in microgrids are used to do the comparisons, as shown in Table 5. In general, the effectiveness of proposed Markov-based reliability evaluation method has been verified through making the comparisons to two other methods. According to the reference [40], the lowest predicted lifetime of the ABESS in the actual DC-coupled configuration is about 19 years which is obvious in a range of 12–57 years of the MTTL from the proposed Markov-based reliability evaluation method. Compared to the reference [32], the overall average failure rate of the ABESS from the proposed method is higher than that of the reference [32], 1.314–2.628 failure per year in comparison with below 1.0 failure per year, respectively. The main reason is that the proposed reliability evaluation method considers both the used-time dependent failure rate and voltage-fluctuation and power-loss dependent failure rate under randomly dynamic operation conditions of the ABESS in the microgrid.

In conclusion, application of the proposed two-step reliability evaluation method to the ABESS can provide the valuable information that is useful to enhance the system-level reliability of microgrids and to

Table 5 The proposed Markov-based reliability evaluation method compared to other existing methods. Reliability evaluation methodologies of the ABESS

Main descriptions

Mean time to failure (years) or the overall failure rate of the ABESS

1. The Markov-based reliability evaluation method for the ABESS with two sub-systems, a DC sub-system and an AC sub-system

- Considering the used-time dependent failure rate and voltage-fluctuation and power-loss dependent failure rate under dynamic conditions; - A clustering technique to the discrete probability distribution model is effectively applied to data points of failure rates of main components in the ABESS. - By performing the reliability analysis on the most reliability-critical components among power conversion units of each configuration; - The dynamic programming method or the Markov model could be used to calculate the reliability. - The DC-coupled configuration is similar to the basic configuration of ABESS proposed. - The lifetime data of the wear out failure is followed by Weibull distribution. - Only considering the used-time dependent failure rate of the BESS during the operational time;

- For both DC and AC loads: the MTFL at 12–57 years; and the overall average failure rate at 1.314–2.628 failure/year; - For only AC loads: the MTFL at 4–50 years; and the overall average failure rate at 1.752–5.256 failure/year;

2. The reliability evaluation method for the ABESS with two actual configuration types, DC- and AC-coupled configurations [40]

3. An analytic approach based on Markov models is applied for the reliability evaluation of BESS, and then is verified by Monte Carlo Simulation method [32];

20

- For the actual DC-coupled configuration: the lowest predicted lifetime is about 19 years which is also in a range of 12–57 years when compared to the proposed Markovbased reliability evaluation method.

- The average failure rate of the BESS is below 1.0 failure per year (to be lower than 1.314–2.628 failure per year from the proposed Markov-based reliability evaluation method).

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maintain or replace battery modules, DC-DC converters, DC-AC inverters, and switching and protective devices in the appropriate times.

Acknowledgement This research was funded by Ministry of Science Technology of the Republic of China, Taiwan, with the grant number of 108-2621-M-033001.

Declaration of Competing Interest The authors declared that there is no conflict of interest. Appendix A (see Table A1) Table A1 Basic specifications of a PV module. Parameters

Values

Maximum power rating (Pmax) Open-circuit voltage, VOC: Nominal operating cell temperature, NOCT: Short-circuit current, ISC: Voltage at maximum power, Vmp: Current at maximum power, Imp:

220 Wp 36.2 V 47 °C 8.20 A 29.7 V 7.39 A

Appendix B (see Table B1) Table B1 Specifications of the bidirectional DC/DC converter. Parameters

Values

Maximum operation power Voltage range at the battery side Voltage range at the DC common bus side Inductor Capacitor Equivalent series resistance (ESR) of the inductor IGBT On resistance Diode on resistance Switching frequency Voltage and current ripples

25 kW 450–550 VDC 750 VDC 1 mH 5–10 μF 0.1 Ω 0.034–0.044 Ω 0.0033 Ω 100 kHz 5%

Appendix C (see Table C1)

Table C1 Basic specifications of the DC/AC inverter. Parameters

Values

Maximum operation power Voltage range at the DC side Voltage range at the AC side Switching frequency Total harmonic distortion (THD)

25 kW 500–750 VDC 220/380 VAC 50 kHz 3.5%

Appendix D. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijepes.2019.105786.

Procedia 2011;5:1284–90. [3] IEEE Guide for Electric Power Distribution Reliability Indices, IEEE Std. 1366™2012, May 2012, DOI: 10.1109/IEEESTD.2012.6209381. [4] Chatzivasileiadi A, Ampatzi E, Knight I. Characteristics of electrical energy storage technologies and their applications in buildings. Renew. Sustain. Energy Rev. 2013;25:814–30. https://doi.org/10.1016/j.rser.2013.05.023.

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